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Block #147,574

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/3/2013, 4:48:23 AM Β· Difficulty 9.8523 Β· 6,660,413 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1a30b64feeb1a4bc281cf8bf2ab6382c4aa86eae5be031abaeff0d294a20cd0c
View on Chainz β†—

Height

#147,574

Difficulty

9.852338

Transactions

1

Size

197 B

Version

2

Bits

09da32d1

Nonce

12,261

Timestamp

9/3/2013, 4:48:23 AM

Confirmations

6,660,413

Mined by

⛏️ P2SHAa6PpN3XWen9U28VLp3hDw33d6XAm9RHxt

Merkle Root

6dd4f623d886bb353b9b85663f448905925309fb2e2db6773f312d84e755a125
Transactions (1)
Coinbase6dd4f623d886bb…312d84e755a125
1 in β†’ 1 out10.2900 XPM109 B
Aa6PpN3X…XAm9RHxt
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.

6.003 Γ— 10⁹⁰(91-digit number)
60032019608791214472…17141624171517224719
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
6.003 Γ— 10⁹⁰(91-digit number)
60032019608791214472…17141624171517224719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.003 Γ— 10⁹⁰(91-digit number)
60032019608791214472…17141624171517224721
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
1.200 Γ— 10⁹¹(92-digit number)
12006403921758242894…34283248343034449439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.200 Γ— 10⁹¹(92-digit number)
12006403921758242894…34283248343034449441
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
2.401 Γ— 10⁹¹(92-digit number)
24012807843516485788…68566496686068898879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.401 Γ— 10⁹¹(92-digit number)
24012807843516485788…68566496686068898881
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
4.802 Γ— 10⁹¹(92-digit number)
48025615687032971577…37132993372137797759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.802 Γ— 10⁹¹(92-digit number)
48025615687032971577…37132993372137797761
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
9.605 Γ— 10⁹¹(92-digit number)
96051231374065943155…74265986744275595519
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:57,707,942 XPMΒ·at block #6,807,986 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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