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Block #162,668

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/13/2013, 11:28:20 AM Β· Difficulty 9.8614 Β· 6,664,253 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f31c5732e0f4efc6af3dab9f41533d7bdcb1a9edcabd9de652f97323a0965f6e
View on Chainz β†—

Height

#162,668

Difficulty

9.861384

Transactions

1

Size

199 B

Version

2

Bits

09dc83ab

Nonce

31,057

Timestamp

9/13/2013, 11:28:20 AM

Confirmations

6,664,253

Mined by

⛏️ P2SHAYkoKAQ4RDKGS7byjZXQArv3A5uuj8DeZs

Merkle Root

a365ad7522eb171b33a7b9070fb732e1765a889840e37a8073cc216cd79e6a72
Transactions (1)
Coinbasea365ad7522eb17…cc216cd79e6a72
1 in β†’ 1 out10.2700 XPM109 B
AYkoKAQ4…uuj8DeZs
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.

3.489 Γ— 10⁹³(94-digit number)
34897637834861942344…62968475461234289399
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
3.489 Γ— 10⁹³(94-digit number)
34897637834861942344…62968475461234289399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.489 Γ— 10⁹³(94-digit number)
34897637834861942344…62968475461234289401
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
6.979 Γ— 10⁹³(94-digit number)
69795275669723884689…25936950922468578799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.979 Γ— 10⁹³(94-digit number)
69795275669723884689…25936950922468578801
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
1.395 Γ— 10⁹⁴(95-digit number)
13959055133944776937…51873901844937157599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.395 Γ— 10⁹⁴(95-digit number)
13959055133944776937…51873901844937157601
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
2.791 Γ— 10⁹⁴(95-digit number)
27918110267889553875…03747803689874315199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.791 Γ— 10⁹⁴(95-digit number)
27918110267889553875…03747803689874315201
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
5.583 Γ— 10⁹⁴(95-digit number)
55836220535779107751…07495607379748630399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,859,539 XPMΒ·at block #6,826,920 Β· updates every 60s
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