Block #240,974

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/2/2013, 10:23:10 PM · Difficulty 9.9575 · 6,589,572 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7217988bb4d414983798dca9e91cd6e13b1af6f2bdbb49d20180a0577ac00c1a

View on Chainz ↗

Height

#240,974

Difficulty

9.957477

Transactions

Size

2.85 KB

Version

Bits

09f51d37

Nonce

21,399

Timestamp

11/2/2013, 10:23:10 PM

Confirmations

6,589,572

Mined by

⛏️ NRu{JAcEnwywzxWFA99sBpHvfDrnmMpvZtt2xTs

Merkle Root

dacb9fa384293875f596003845dd27be6de95647dbb545e593a430bf457778a3

Transactions (4)

Coinbasecb2b1cf22af77e…66014d9aae320e

1 in → 45 out10.0484 XPM1.55 KB

AcEnwywz…vZtt2xTs APVGazMT…cDCk2nwA ANuKx9Ke…wm7nrBRq ANo4YY1x…vnsPRDSU ARanXFdq…2FNquU2w

dbf290bd46ed2e…ffa2bc63fd73d5

3 in → 2 out30.2500 XPM522 B

Abxn3EEB…8ccf7zVj AemFZRDd…mk9yku2W

e54b67dda7a76e…8a1a136267d754

1 in → 2 out10.0700 XPM193 B

AH788BG7…EpaWNQ4V AQAvQSWZ…C9mFkvux

aef1f349afb1c3…47c57eff59d1d0

3 in → 2 out28.2153 XPM523 B

AezMhRvq…8Rrp4t6G AN7ZnJS4…uHpiPac9

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.

1.404 × 10⁹⁰(91-digit number)

14041712956229533469…99878620498094535999

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

1.404 × 10⁹⁰(91-digit number)

14041712956229533469…99878620498094535999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.404 × 10⁹⁰(91-digit number)

14041712956229533469…99878620498094536001

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

2.808 × 10⁹⁰(91-digit number)

28083425912459066939…99757240996189071999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.808 × 10⁹⁰(91-digit number)

28083425912459066939…99757240996189072001

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

5.616 × 10⁹⁰(91-digit number)

56166851824918133879…99514481992378143999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.616 × 10⁹⁰(91-digit number)

56166851824918133879…99514481992378144001

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

1.123 × 10⁹¹(92-digit number)

11233370364983626775…99028963984756287999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.123 × 10⁹¹(92-digit number)

11233370364983626775…99028963984756288001

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

2.246 × 10⁹¹(92-digit number)

22466740729967253551…98057927969512575999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.246 × 10⁹¹(92-digit number)

22466740729967253551…98057927969512576001

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #240,974

Cookie Preferences