Block #654,728

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/30/2014, 10:06:22 AM · Difficulty 10.9552 · 6,145,795 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a5ea56ea5561114042dada78c8edc209a322bb857b2413fd637bd414495cb636

View on Chainz ↗

Height

#654,728

Difficulty

10.955241

Transactions

Size

693 B

Version

Bits

0af48aa9

Nonce

144,252,994

Timestamp

7/30/2014, 10:06:22 AM

Confirmations

6,145,795

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e9b333e5bee560212949223b2250d4749d2a8b4580196b8e927a7782624b80b9

Transactions (3)

Coinbase15e8a32f70395b…e02825a32eae7e

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

a83b5dde1800a6…10ec4fbbf7bbf0

1 in → 3 out4.1419 XPM260 B

AcNovFbg…sJ1oLH5E AeKNrjNj…1NEq95Ta AHZ6LSRb…otxTNghi

12aa06e57e0847…58bb9bf209c4e6

1 in → 2 out3.7571 XPM226 B

AGSDmYMR…HAssTToc ALDzdy5Q…23FbHCPU

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.

1.507 × 10⁹⁶(97-digit number)

15076300398242919353…93098815602696806399

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

1.507 × 10⁹⁶(97-digit number)

15076300398242919353…93098815602696806399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.507 × 10⁹⁶(97-digit number)

15076300398242919353…93098815602696806401

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

3.015 × 10⁹⁶(97-digit number)

30152600796485838707…86197631205393612799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.015 × 10⁹⁶(97-digit number)

30152600796485838707…86197631205393612801

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

6.030 × 10⁹⁶(97-digit number)

60305201592971677414…72395262410787225599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.030 × 10⁹⁶(97-digit number)

60305201592971677414…72395262410787225601

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

1.206 × 10⁹⁷(98-digit number)

12061040318594335482…44790524821574451199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.206 × 10⁹⁷(98-digit number)

12061040318594335482…44790524821574451201

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

2.412 × 10⁹⁷(98-digit number)

24122080637188670965…89581049643148902399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.412 × 10⁹⁷(98-digit number)

24122080637188670965…89581049643148902401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.824 × 10⁹⁷(98-digit number)

48244161274377341931…79162099286297804799

Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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

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 × 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