Block #428,073

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/3/2014, 7:57:02 PM · Difficulty 10.3480 · 6,366,675 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2fee02084ba6f40846d52687c335c86df837611dccead37143ad4cef9019d6cc

View on Chainz ↗

Height

#428,073

Difficulty

10.347983

Transactions

Size

1.23 KB

Version

Bits

0a591567

Nonce

54,832

Timestamp

3/3/2014, 7:57:02 PM

Confirmations

6,366,675

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

345b0eed87b85c5af59a7b34dc42af58e38060278bd1564e00240e8424a96746

Transactions (2)

Coinbasead2b75260bc690…2508e223b441af

1 in → 1 out9.3400 XPM110 B

AeKNrjNj…1NEq95Ta

6598391d9f8352…eab2c9ae911abd

5 in → 13 out39.2496 XPM1.03 KB

AZHEpaqf…MxbjTDc5 AG75JD8M…YE8Hjvb7 Acag3ba1…JAWgJwcR AJ1Rg4tk…5YkqEmTH AXtUqJwy…tydVS7cu

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.

1.096 × 10¹⁰²(103-digit number)

10960483767163840069…33992075561394706999

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

1.096 × 10¹⁰²(103-digit number)

10960483767163840069…33992075561394706999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.096 × 10¹⁰²(103-digit number)

10960483767163840069…33992075561394707001

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

2.192 × 10¹⁰²(103-digit number)

21920967534327680138…67984151122789413999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.192 × 10¹⁰²(103-digit number)

21920967534327680138…67984151122789414001

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

4.384 × 10¹⁰²(103-digit number)

43841935068655360277…35968302245578827999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.384 × 10¹⁰²(103-digit number)

43841935068655360277…35968302245578828001

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

8.768 × 10¹⁰²(103-digit number)

87683870137310720554…71936604491157655999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.768 × 10¹⁰²(103-digit number)

87683870137310720554…71936604491157656001

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

1.753 × 10¹⁰³(104-digit number)

17536774027462144110…43873208982315311999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.753 × 10¹⁰³(104-digit number)

17536774027462144110…43873208982315312001

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

3.507 × 10¹⁰³(104-digit number)

35073548054924288221…87746417964630623999

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