Block #314,950

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/16/2013, 6:18:21 AM · Difficulty 10.0792 · 6,484,072 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b907c9fc95e9398851346d0ef3a700c56a6fc063fe95d9efdeb55392e2b16108

View on Chainz ↗

Height

#314,950

Difficulty

10.079182

Transactions

Size

1.64 KB

Version

Bits

0a14453e

Nonce

147,378

Timestamp

12/16/2013, 6:18:21 AM

Confirmations

6,484,072

Mined by

⛏️ FaRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

4afb78a0d96bd66888cc5d5fd65eae9e3e2c8c185fc5a8f8cf0bd06623b0e11f

Transactions (4)

Coinbase34ea47b2a476ed…4205da4d8134bc

1 in → 25 out9.8300 XPM913 B

Aac9Hjdg…P4ktypc3 AJzWx2VD…j4ZSMit5 AWXYBWKP…qQAoisBJ AcC2zSod…rtWatH79 AcaLouCs…xPDq8Sis

fe25caa78b4815…5aa33c27d46ae9

1 in → 2 out6.7979 XPM226 B

ASTXicGA…V1vGz5RK AHsyhmcE…ZLisLzkw

64231e30dd344d…0cd0ca5a7ddfd5

1 in → 2 out3.8932 XPM226 B

AWGQhzDN…RDYvugUy AevUcmun…MaEs2FRy

25775f9b71170e…809bc071d518ab

1 in → 2 out3.8230 XPM226 B

ATHR6oPB…CWcCmaGW AZ727oip…YNSBb9rF

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.

2.456 × 10⁹⁹(100-digit number)

24565454904517749720…11304823863279491519

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

2.456 × 10⁹⁹(100-digit number)

24565454904517749720…11304823863279491519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.456 × 10⁹⁹(100-digit number)

24565454904517749720…11304823863279491521

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

4.913 × 10⁹⁹(100-digit number)

49130909809035499441…22609647726558983039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.913 × 10⁹⁹(100-digit number)

49130909809035499441…22609647726558983041

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

9.826 × 10⁹⁹(100-digit number)

98261819618070998882…45219295453117966079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.826 × 10⁹⁹(100-digit number)

98261819618070998882…45219295453117966081

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

1.965 × 10¹⁰⁰(101-digit number)

19652363923614199776…90438590906235932159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.965 × 10¹⁰⁰(101-digit number)

19652363923614199776…90438590906235932161

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

3.930 × 10¹⁰⁰(101-digit number)

39304727847228399553…80877181812471864319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.930 × 10¹⁰⁰(101-digit number)

39304727847228399553…80877181812471864321

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