Block #610,525

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/1/2014, 6:10:48 PM · Difficulty 10.9175 · 6,202,312 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e8078e9ab8942c8c739440c6b0bfd4a17c3e56884d105787ea1204378a9cc540

View on Chainz ↗

Height

#610,525

Difficulty

10.917456

Transactions

Size

582 B

Version

Bits

0aeade65

Nonce

245,994,179

Timestamp

7/1/2014, 6:10:48 PM

Confirmations

6,202,312

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5fa9f1516414c59bcd4d85c17bd4db0849f2525be75c1765f7f0b831a79e548f

Transactions (2)

Coinbase8c67eecf734755…521a9d9edbac8a

1 in → 1 out8.3900 XPM116 B

ANSXnLY2…Sd25TjkD

469c8d8aba5b86…307591c6bcc152

2 in → 2 out6.0690 XPM374 B

AUKkA6c6…kGHhpssL AFpAkagB…qre8cig8

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.

2.182 × 10⁹⁹(100-digit number)

21823213512793118204…34463513818533887999

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

2.182 × 10⁹⁹(100-digit number)

21823213512793118204…34463513818533887999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.182 × 10⁹⁹(100-digit number)

21823213512793118204…34463513818533888001

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

4.364 × 10⁹⁹(100-digit number)

43646427025586236408…68927027637067775999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.364 × 10⁹⁹(100-digit number)

43646427025586236408…68927027637067776001

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

8.729 × 10⁹⁹(100-digit number)

87292854051172472817…37854055274135551999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.729 × 10⁹⁹(100-digit number)

87292854051172472817…37854055274135552001

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

1.745 × 10¹⁰⁰(101-digit number)

17458570810234494563…75708110548271103999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.745 × 10¹⁰⁰(101-digit number)

17458570810234494563…75708110548271104001

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

3.491 × 10¹⁰⁰(101-digit number)

34917141620468989127…51416221096542207999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.491 × 10¹⁰⁰(101-digit number)

34917141620468989127…51416221096542208001

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

6.983 × 10¹⁰⁰(101-digit number)

69834283240937978254…02832442193084415999

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

Block #610,525

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