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Block #27,047

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 7:27:31 AM Β· Difficulty 7.9775 Β· 6,779,003 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3f31a63e961f96b4559dcb5fa4f1ec78f4bba3789d1cb77e05c08fb8bc34e751
View on Chainz β†—

Height

#27,047

Difficulty

7.977464

Transactions

1

Size

196 B

Version

2

Bits

07fa3b0e

Nonce

49

Timestamp

7/13/2013, 7:27:31 AM

Confirmations

6,779,003

Mined by

⛏️ P2SHAYHAf9fPjqz1L6Mm5PTCxewRgPREXAP7eS

Merkle Root

bd3d7f016a6594892f5e74a09b2b78c813671f3871a4907dfb827beea5a83742
Transactions (1)
Coinbasebd3d7f016a6594…827beea5a83742
1 in β†’ 1 out15.6900 XPM108 B
AYHAf9fP…REXAP7eS
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.

9.536 Γ— 10⁸⁹(90-digit number)
95361139022360134455…44947052424634795749
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
9.536 Γ— 10⁸⁹(90-digit number)
95361139022360134455…44947052424634795749
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.536 Γ— 10⁸⁹(90-digit number)
95361139022360134455…44947052424634795751
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
1.907 Γ— 10⁹⁰(91-digit number)
19072227804472026891…89894104849269591499
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.907 Γ— 10⁹⁰(91-digit number)
19072227804472026891…89894104849269591501
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
3.814 Γ— 10⁹⁰(91-digit number)
38144455608944053782…79788209698539182999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.814 Γ— 10⁹⁰(91-digit number)
38144455608944053782…79788209698539183001
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
7.628 Γ— 10⁹⁰(91-digit number)
76288911217888107564…59576419397078365999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.628 Γ— 10⁹⁰(91-digit number)
76288911217888107564…59576419397078366001
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
1.525 Γ— 10⁹¹(92-digit number)
15257782243577621512…19152838794156731999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9

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:57,692,482 XPMΒ·at block #6,806,049 Β· updates every 60s
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