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Block #134,147

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/25/2013, 9:53:34 PM Β· Difficulty 9.8009 Β· 6,675,762 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e887c5a2149d41bb67d2428e1017f1470768bcd51853534e9b479601dd83d29a
View on Chainz β†—

Height

#134,147

Difficulty

9.800866

Transactions

1

Size

201 B

Version

2

Bits

09cd0589

Nonce

18,390

Timestamp

8/25/2013, 9:53:34 PM

Confirmations

6,675,762

Mined by

⛏️ P2SHAcecj4WYP2kTRjXJMUTPed41WTwKtCNbS5

Merkle Root

0bfcb938204cc6a7ed1172742b7879dc99a772c6e17028c0aa1c171f42ca1b20
Transactions (1)
Coinbase0bfcb938204cc6…1c171f42ca1b20
1 in β†’ 1 out10.4000 XPM109 B
Acecj4WY…wKtCNbS5
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.567 Γ— 10⁹⁸(99-digit number)
55676423014598126457…03671980538698237439
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
5.567 Γ— 10⁹⁸(99-digit number)
55676423014598126457…03671980538698237439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.567 Γ— 10⁹⁸(99-digit number)
55676423014598126457…03671980538698237441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.113 Γ— 10⁹⁹(100-digit number)
11135284602919625291…07343961077396474879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.113 Γ— 10⁹⁹(100-digit number)
11135284602919625291…07343961077396474881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.227 Γ— 10⁹⁹(100-digit number)
22270569205839250582…14687922154792949759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.227 Γ— 10⁹⁹(100-digit number)
22270569205839250582…14687922154792949761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
4.454 Γ— 10⁹⁹(100-digit number)
44541138411678501165…29375844309585899519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.454 Γ— 10⁹⁹(100-digit number)
44541138411678501165…29375844309585899521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
8.908 Γ— 10⁹⁹(100-digit number)
89082276823357002331…58751688619171799039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.908 Γ— 10⁹⁹(100-digit number)
89082276823357002331…58751688619171799041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,723,355 XPMΒ·at block #6,809,908 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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