Block #53,920

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/16/2013, 5:46:01 PM · Difficulty 8.9285 · 6,738,044 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dca8abcc4fd5f90396c346b41c4584b6e78d9088d472fb134c69c19bd581f0a9

View on Chainz ↗

Height

#53,920

Difficulty

8.928483

Transactions

Size

209 B

Version

Bits

08edb112

Nonce

936

Timestamp

7/16/2013, 5:46:01 PM

Confirmations

6,738,044

Merkle Root

81c86b108b42ebb81a426264205ddc0ec99f16912e1165ea001b99e07e4a2786

Transactions (1)

Coinbase81c86b108b42eb…1b99e07e4a2786

1 in → 1 out12.5300 XPM110 B

AQEbmWMh…bVPpCt5X

Prime Chain Origin

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

1.112 × 10¹¹⁷(118-digit number)

11125037537931759733…56706792409586191839

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

1.112 × 10¹¹⁷(118-digit number)

11125037537931759733…56706792409586191839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.112 × 10¹¹⁷(118-digit number)

11125037537931759733…56706792409586191841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

2.225 × 10¹¹⁷(118-digit number)

22250075075863519467…13413584819172383679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.225 × 10¹¹⁷(118-digit number)

22250075075863519467…13413584819172383681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

4.450 × 10¹¹⁷(118-digit number)

44500150151727038934…26827169638344767359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.450 × 10¹¹⁷(118-digit number)

44500150151727038934…26827169638344767361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

8.900 × 10¹¹⁷(118-digit number)

89000300303454077868…53654339276689534719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.900 × 10¹¹⁷(118-digit number)

89000300303454077868…53654339276689534721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.780 × 10¹¹⁸(119-digit number)

17800060060690815573…07308678553379069439

Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer