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Block #641,075

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 7/20/2014, 5:20:18 PM Β· Difficulty 10.9576 Β· 6,176,777 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
64031377dd30b45ae14e40cd67a4f264d345c9cbc7581ab1a007a16ad43949d0
View on Chainz β†—

Height

#641,075

Difficulty

10.957572

Transactions

2

Size

545 B

Version

2

Bits

0af5236a

Nonce

1,620,049,742

Timestamp

7/20/2014, 5:20:18 PM

Confirmations

6,176,777

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b617808cb7fa37d2a089402dba5b04852bf8db5f98955504183c869ab4a68272
Transactions (2)
Coinbase4e6ea6856904c4…78a4b8db917f05
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
e31fbb3768ced4…ac7fa8f4876a64
2 in β†’ 1 out4.9963 XPM338 B
ATN6eQLm…hMs7kfrJ
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.609 Γ— 10⁹⁷(98-digit number)
26092294358149361473…99535564830278100159
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.609 Γ— 10⁹⁷(98-digit number)
26092294358149361473…99535564830278100159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.609 Γ— 10⁹⁷(98-digit number)
26092294358149361473…99535564830278100161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
5.218 Γ— 10⁹⁷(98-digit number)
52184588716298722946…99071129660556200319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.218 Γ— 10⁹⁷(98-digit number)
52184588716298722946…99071129660556200321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.043 Γ— 10⁹⁸(99-digit number)
10436917743259744589…98142259321112400639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.043 Γ— 10⁹⁸(99-digit number)
10436917743259744589…98142259321112400641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
2.087 Γ— 10⁹⁸(99-digit number)
20873835486519489178…96284518642224801279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.087 Γ— 10⁹⁸(99-digit number)
20873835486519489178…96284518642224801281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
4.174 Γ— 10⁹⁸(99-digit number)
41747670973038978357…92569037284449602559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.174 Γ— 10⁹⁸(99-digit number)
41747670973038978357…92569037284449602561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
8.349 Γ— 10⁹⁸(99-digit number)
83495341946077956714…85138074568899205119
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
8.349 Γ— 10⁹⁸(99-digit number)
83495341946077956714…85138074568899205121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,786,882 XPMΒ·at block #6,817,851 Β· updates every 60s
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