Block #27,528

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 9:08:47 AM · Difficulty 7.9791 · 6,779,932 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de73e54b525e4ce0beaec0bcb11cd045f11665be1c5f3e12539c1acc4d1ca2f2

View on Chainz ↗

Height

#27,528

Difficulty

7.979114

Transactions

Size

1.90 KB

Version

Bits

07faa731

Nonce

Timestamp

7/13/2013, 9:08:47 AM

Confirmations

6,779,932

Mined by

⛏️ P2SHAWn9ZZUHtuEtAU94ksXk6sBraP53EQdG3f

Merkle Root

1d04c5e5b63038483c7239b3ff66d4cc5c47fdb428663d6bbd17c8dbf4f4438f

Transactions (2)

Coinbase41f8fb36011b3a…7c90105e736259

1 in → 1 out15.7100 XPM108 B

AWn9ZZUH…53EQdG3f

49ffac8fc0d0d9…05f19d9af1531c

14 in → 2 out200.9700 XPM1.70 KB

AHKzbhte…zdMNRaZX AduwKP5J…wp1LyLxL

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.

3.443 × 10¹⁰³(104-digit number)

34438565499766272515…14027593085026787989

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

3.443 × 10¹⁰³(104-digit number)

34438565499766272515…14027593085026787989

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.443 × 10¹⁰³(104-digit number)

34438565499766272515…14027593085026787991

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

6.887 × 10¹⁰³(104-digit number)

68877130999532545030…28055186170053575979

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.887 × 10¹⁰³(104-digit number)

68877130999532545030…28055186170053575981

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

1.377 × 10¹⁰⁴(105-digit number)

13775426199906509006…56110372340107151959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.377 × 10¹⁰⁴(105-digit number)

13775426199906509006…56110372340107151961

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

2.755 × 10¹⁰⁴(105-digit number)

27550852399813018012…12220744680214303919

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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

Block #27,528

Cookie Preferences