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Block #141,574

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/30/2013, 10:05:06 AM Β· Difficulty 9.8349 Β· 6,667,508 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b1c5139a31c1e9455eaa57c8cf37da64b3366b581ce9874498d4bc53b9a746d8
View on Chainz β†—

Height

#141,574

Difficulty

9.834898

Transactions

2

Size

389 B

Version

2

Bits

09d5bbdc

Nonce

64,736

Timestamp

8/30/2013, 10:05:06 AM

Confirmations

6,667,508

Mined by

⛏️ P2SHAMRUwRsTQ2rEZmGrKsmy5yqDMLsc7CJatb

Merkle Root

e1643681a83233f42c810e4b7b849ca211469170ef23ac7ce44193fc7296d913
Transactions (2)
Coinbase49fbe1f0d0c34e…4454559aeb83ca
1 in β†’ 1 out10.3300 XPM109 B
AMRUwRsT…sc7CJatb
8b4c477f468686…1dbcfc3074d1e6
1 in β†’ 1 out1.9940 XPM192 B
AKjsjTkW…7rGbLvxN
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.

1.164 Γ— 10⁹⁰(91-digit number)
11641974440782173179…65401589858728321599
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
1.164 Γ— 10⁹⁰(91-digit number)
11641974440782173179…65401589858728321599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.164 Γ— 10⁹⁰(91-digit number)
11641974440782173179…65401589858728321601
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
2.328 Γ— 10⁹⁰(91-digit number)
23283948881564346358…30803179717456643199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.328 Γ— 10⁹⁰(91-digit number)
23283948881564346358…30803179717456643201
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
4.656 Γ— 10⁹⁰(91-digit number)
46567897763128692716…61606359434913286399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.656 Γ— 10⁹⁰(91-digit number)
46567897763128692716…61606359434913286401
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
9.313 Γ— 10⁹⁰(91-digit number)
93135795526257385433…23212718869826572799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.313 Γ— 10⁹⁰(91-digit number)
93135795526257385433…23212718869826572801
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
1.862 Γ— 10⁹¹(92-digit number)
18627159105251477086…46425437739653145599
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:57,716,718 XPMΒ·at block #6,809,081 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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