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Block #150,760

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2013, 6:18:38 AM Β· Difficulty 9.8587 Β· 6,659,164 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b2e42e65c1895e56e425928e6c14f0a5262946a0d5e70183d111ae75d2f2178e
View on Chainz β†—

Height

#150,760

Difficulty

9.858730

Transactions

1

Size

198 B

Version

2

Bits

09dbd5c1

Nonce

68,799

Timestamp

9/5/2013, 6:18:38 AM

Confirmations

6,659,164

Mined by

⛏️ P2SHAJQ7bqzh8jMKwbhminzZ7vurTxoY2ANRaW

Merkle Root

2f5db78e098fc805a7a6fe28e8e4f9c379c8ff2ca224cc399599c2f0df28294a
Transactions (1)
Coinbase2f5db78e098fc8…99c2f0df28294a
1 in β†’ 1 out10.2700 XPM109 B
AJQ7bqzh…oY2ANRaW
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.

1.637 Γ— 10⁹³(94-digit number)
16375058103972252177…45389276460541224959
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
1.637 Γ— 10⁹³(94-digit number)
16375058103972252177…45389276460541224959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.637 Γ— 10⁹³(94-digit number)
16375058103972252177…45389276460541224961
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
3.275 Γ— 10⁹³(94-digit number)
32750116207944504355…90778552921082449919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.275 Γ— 10⁹³(94-digit number)
32750116207944504355…90778552921082449921
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
6.550 Γ— 10⁹³(94-digit number)
65500232415889008711…81557105842164899839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.550 Γ— 10⁹³(94-digit number)
65500232415889008711…81557105842164899841
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
1.310 Γ— 10⁹⁴(95-digit number)
13100046483177801742…63114211684329799679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.310 Γ— 10⁹⁴(95-digit number)
13100046483177801742…63114211684329799681
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
2.620 Γ— 10⁹⁴(95-digit number)
26200092966355603484…26228423368659599359
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:57,723,478 XPMΒ·at block #6,809,923 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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