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Block #2,807,676

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 8/24/2018, 8:04:34 AM Β· Difficulty 11.6734 Β· 4,033,499 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ab7fba879f383d210771cb4fe6b562ad2c9bb2db83d8e655db43f0ffe4922000
View on Chainz β†—

Height

#2,807,676

Difficulty

11.673387

Transactions

1

Size

201 B

Version

2

Bits

0bac631c

Nonce

1,894,186,918

Timestamp

8/24/2018, 8:04:34 AM

Confirmations

4,033,499

Mined by

⛏️ P2SHAKfojTyYrvRXtRjwyXhMRRBEg6VnG8wmX8

Merkle Root

65501e26962eb473f47f94ea0b3cd1c931772ee18ce8f22320ba3abf213be9b9
Transactions (1)
Coinbase65501e26962eb4…ba3abf213be9b9
1 in β†’ 1 out7.3300 XPM110 B
AKfojTyY…VnG8wmX8
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.

1.085 Γ— 10⁹⁷(98-digit number)
10853352421647133372…99879904287876026879
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
1.085 Γ— 10⁹⁷(98-digit number)
10853352421647133372…99879904287876026879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.085 Γ— 10⁹⁷(98-digit number)
10853352421647133372…99879904287876026881
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
2.170 Γ— 10⁹⁷(98-digit number)
21706704843294266745…99759808575752053759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.170 Γ— 10⁹⁷(98-digit number)
21706704843294266745…99759808575752053761
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
4.341 Γ— 10⁹⁷(98-digit number)
43413409686588533491…99519617151504107519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.341 Γ— 10⁹⁷(98-digit number)
43413409686588533491…99519617151504107521
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
8.682 Γ— 10⁹⁷(98-digit number)
86826819373177066983…99039234303008215039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.682 Γ— 10⁹⁷(98-digit number)
86826819373177066983…99039234303008215041
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
1.736 Γ— 10⁹⁸(99-digit number)
17365363874635413396…98078468606016430079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.736 Γ— 10⁹⁸(99-digit number)
17365363874635413396…98078468606016430081
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
3.473 Γ— 10⁹⁸(99-digit number)
34730727749270826793…96156937212032860159
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
3.473 Γ— 10⁹⁸(99-digit number)
34730727749270826793…96156937212032860161
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:57,973,758 XPMΒ·at block #6,841,174 Β· updates every 60s
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