Block #210,607

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/15/2013, 6:21:27 AM · Difficulty 9.9131 · 6,584,772 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0efed1564a4c2e54977e123b94bc6860a6d9c3d0d2bf54141aaf109474982f65

View on Chainz ↗

Height

#210,607

Difficulty

9.913088

Transactions

Size

202 B

Version

Bits

09e9c021

Nonce

18,537

Timestamp

10/15/2013, 6:21:27 AM

Confirmations

6,584,772

Mined by

⛏️ P2SHAH8MuWecApb7HmsNwfd9UPDw7y2bVG62mK

Merkle Root

bf998ef22544f3c9b07ea0e3a646caa09356edaa0fb48f5b0bd9d415c8232a7e

Transactions (1)

Coinbasebf998ef22544f3…d9d415c8232a7e

1 in → 1 out10.1600 XPM109 B

AH8MuWec…2bVG62mK

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.

1.714 × 10¹⁰¹(102-digit number)

17147196895797684370…57244280135602727439

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

1.714 × 10¹⁰¹(102-digit number)

17147196895797684370…57244280135602727439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.714 × 10¹⁰¹(102-digit number)

17147196895797684370…57244280135602727441

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

3.429 × 10¹⁰¹(102-digit number)

34294393791595368740…14488560271205454879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.429 × 10¹⁰¹(102-digit number)

34294393791595368740…14488560271205454881

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

6.858 × 10¹⁰¹(102-digit number)

68588787583190737481…28977120542410909759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.858 × 10¹⁰¹(102-digit number)

68588787583190737481…28977120542410909761

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

1.371 × 10¹⁰²(103-digit number)

13717757516638147496…57954241084821819519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.371 × 10¹⁰²(103-digit number)

13717757516638147496…57954241084821819521

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

2.743 × 10¹⁰²(103-digit number)

27435515033276294992…15908482169643639039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.743 × 10¹⁰²(103-digit number)

27435515033276294992…15908482169643639041

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

5.487 × 10¹⁰²(103-digit number)

54871030066552589985…31816964339287278079

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