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Block #60,373

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/18/2013, 7:37:05 AM Β· Difficulty 8.9689 Β· 6,755,590 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
eafb5c2743129a02c168b79e0e2c4129ccfd6186c3d5b7df7c9bd0fa395f3528
View on Chainz β†—

Height

#60,373

Difficulty

8.968943

Transactions

1

Size

201 B

Version

2

Bits

08f80cae

Nonce

304

Timestamp

7/18/2013, 7:37:05 AM

Confirmations

6,755,590

Mined by

⛏️ P2SHAXhusrn1VuAD4LsRtSVEeyXGAUAbiGqo2E

Merkle Root

95761bdd9aa981a48849fefa8b13c65b65a97254d51087a967b6c32b0ceb8194
Transactions (1)
Coinbase95761bdd9aa981…b6c32b0ceb8194
1 in β†’ 1 out12.4100 XPM110 B
AXhusrn1…AbiGqo2E
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.

2.394 Γ— 10⁹⁸(99-digit number)
23948978876160600338…14426221401126623999
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
2.394 Γ— 10⁹⁸(99-digit number)
23948978876160600338…14426221401126623999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.394 Γ— 10⁹⁸(99-digit number)
23948978876160600338…14426221401126624001
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
4.789 Γ— 10⁹⁸(99-digit number)
47897957752321200676…28852442802253247999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.789 Γ— 10⁹⁸(99-digit number)
47897957752321200676…28852442802253248001
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
9.579 Γ— 10⁹⁸(99-digit number)
95795915504642401353…57704885604506495999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.579 Γ— 10⁹⁸(99-digit number)
95795915504642401353…57704885604506496001
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
1.915 Γ— 10⁹⁹(100-digit number)
19159183100928480270…15409771209012991999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.915 Γ— 10⁹⁹(100-digit number)
19159183100928480270…15409771209012992001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,771,819 XPMΒ·at block #6,815,962 Β· updates every 60s
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