Block #474,468

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2014, 2:30:05 PM · Difficulty 10.4520 · 6,336,046 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a296794e89ec42814d43d8ac51f4871b0f5340985c00653dddd13c91b865ad09

View on Chainz ↗

Height

#474,468

Difficulty

10.451991

Transactions

Size

2.29 KB

Version

Bits

0a73b5a7

Nonce

65,109

Timestamp

4/4/2014, 2:30:05 PM

Confirmations

6,336,046

Mined by

⛏️ d=1AGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

d61c9a26b1857c524d2dac2d4e54a30702cf47dffd6a6e9ac16713a217ca36cd

Transactions (4)

Coinbase51e2cfe7c0256e…2738b25d6eaf70

1 in → 21 out9.1800 XPM777 B

AGz9gyZW…bo8NYQpw AdFLJFhb…bsaVkAyh AMW1p9oT…2TzdaZxH ATp4jJhs…TbSgR8Qb AbHY4iza…Yckt2J5W

c3dbb99ad7f68a…2e0b9eae4f9480

5 in → 11 out32.2146 XPM1023 B

Ab6WKLJE…gSLntrmQ AXW5oy9W…fVjVrfCH AVYSUn6n…gcdzE7B1 Aa2eBMM4…Pb5hahKv AeKNrjNj…1NEq95Ta

01e3a63582d546…e74b2c476d9944

1 in → 2 out5.1094 XPM225 B

AX3E51X3…GNiwVpH6 AP9CtVJc…YJQcZetr

c6099d4fe669ae…d279ee840950ba

1 in → 2 out2.5985 XPM226 B

ASKmXkrq…4Z94Uumh AbEE5twh…NaGWG2MG

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.

1.045 × 10⁹⁵(96-digit number)

10450103462411254854…95702845344837119999

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

1.045 × 10⁹⁵(96-digit number)

10450103462411254854…95702845344837119999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.045 × 10⁹⁵(96-digit number)

10450103462411254854…95702845344837120001

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

2.090 × 10⁹⁵(96-digit number)

20900206924822509709…91405690689674239999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.090 × 10⁹⁵(96-digit number)

20900206924822509709…91405690689674240001

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

4.180 × 10⁹⁵(96-digit number)

41800413849645019419…82811381379348479999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.180 × 10⁹⁵(96-digit number)

41800413849645019419…82811381379348480001

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

8.360 × 10⁹⁵(96-digit number)

83600827699290038839…65622762758696959999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.360 × 10⁹⁵(96-digit number)

83600827699290038839…65622762758696960001

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

1.672 × 10⁹⁶(97-digit number)

16720165539858007767…31245525517393919999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.672 × 10⁹⁶(97-digit number)

16720165539858007767…31245525517393920001

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 #474,468

Cookie Preferences