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Block #151,689

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2013, 8:11:56 PM Β· Difficulty 9.8614 Β· 6,654,164 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c5f291b8c7a81050cc4cbd7ac3c96010730fb85296d85f4fce4f9c2b21c4c09d
View on Chainz β†—

Height

#151,689

Difficulty

9.861427

Transactions

2

Size

357 B

Version

2

Bits

09dc8683

Nonce

20,388

Timestamp

9/5/2013, 8:11:56 PM

Confirmations

6,654,164

Mined by

⛏️ P2SHAJDBC5H9UmxYNK1DGJSKrActBGp2ZXuna5

Merkle Root

91990a0495c351136667d8032711441155bb50a35e6f4fdd1186a77c7e64c23a
Transactions (2)
Coinbasef656fbab63ca9f…7fd1dc1aa672fb
1 in β†’ 1 out10.2800 XPM109 B
AJDBC5H9…p2ZXuna5
2c0e10dc483c2a…99bb5e2419f587
1 in β†’ 1 out10.3100 XPM157 B
Abg9b4kX…im9CLs7g
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.

1.031 Γ— 10⁹⁷(98-digit number)
10317538732518270452…18255185261463300479
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
1.031 Γ— 10⁹⁷(98-digit number)
10317538732518270452…18255185261463300479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.031 Γ— 10⁹⁷(98-digit number)
10317538732518270452…18255185261463300481
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
2.063 Γ— 10⁹⁷(98-digit number)
20635077465036540905…36510370522926600959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.063 Γ— 10⁹⁷(98-digit number)
20635077465036540905…36510370522926600961
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
4.127 Γ— 10⁹⁷(98-digit number)
41270154930073081810…73020741045853201919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.127 Γ— 10⁹⁷(98-digit number)
41270154930073081810…73020741045853201921
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
8.254 Γ— 10⁹⁷(98-digit number)
82540309860146163621…46041482091706403839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.254 Γ— 10⁹⁷(98-digit number)
82540309860146163621…46041482091706403841
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
1.650 Γ— 10⁹⁸(99-digit number)
16508061972029232724…92082964183412807679
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:57,690,905 XPMΒ·at block #6,805,852 Β· updates every 60s
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