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Block #555,431

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/21/2014, 1:49:51 PM Β· Difficulty 10.9627 Β· 6,269,989 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
05cdf1f4b16a9084390ff8e795bda3d4d4918336442630133301b3e7603ba396
View on Chainz β†—

Height

#555,431

Difficulty

10.962704

Transactions

2

Size

3.74 KB

Version

2

Bits

0af673cc

Nonce

33,447,452

Timestamp

5/21/2014, 1:49:51 PM

Confirmations

6,269,989

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9a97131ff8126550f34a9255f6db1dda2094385d61bfb1dd8432bc59b1e42e08
Transactions (2)
Coinbasee7909840dbd1b6…80085412d8bfd1
1 in β†’ 1 out8.3700 XPM116 B
ANSXnLY2…Sd25TjkD
a3689a9daabc9a…e51713be6fed6c
24 in β†’ 2 out5000.0100 XPM3.54 KB
Ae5WFHbn…gBo7rvHrAVfzUW1X…p4CruZPY
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.

8.015 Γ— 10⁹⁢(97-digit number)
80155974231659855780…80094482147810228749
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
8.015 Γ— 10⁹⁢(97-digit number)
80155974231659855780…80094482147810228749
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.015 Γ— 10⁹⁢(97-digit number)
80155974231659855780…80094482147810228751
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
1.603 Γ— 10⁹⁷(98-digit number)
16031194846331971156…60188964295620457499
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.603 Γ— 10⁹⁷(98-digit number)
16031194846331971156…60188964295620457501
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
3.206 Γ— 10⁹⁷(98-digit number)
32062389692663942312…20377928591240914999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.206 Γ— 10⁹⁷(98-digit number)
32062389692663942312…20377928591240915001
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
6.412 Γ— 10⁹⁷(98-digit number)
64124779385327884624…40755857182481829999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.412 Γ— 10⁹⁷(98-digit number)
64124779385327884624…40755857182481830001
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
1.282 Γ— 10⁹⁸(99-digit number)
12824955877065576924…81511714364963659999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.282 Γ— 10⁹⁸(99-digit number)
12824955877065576924…81511714364963660001
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
2.564 Γ— 10⁹⁸(99-digit number)
25649911754131153849…63023428729927319999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,847,461 XPMΒ·at block #6,825,419 Β· updates every 60s
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