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Block #147,973

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/3/2013, 10:43:39 AM Β· Difficulty 9.8537 Β· 6,657,264 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fbb5935920c6adaeae90de7a08f1dea84f663acbaffd745016dbd50685b9cdb1
View on Chainz β†—

Height

#147,973

Difficulty

9.853698

Transactions

1

Size

197 B

Version

2

Bits

09da8bf4

Nonce

304,042

Timestamp

9/3/2013, 10:43:39 AM

Confirmations

6,657,264

Mined by

⛏️ P2SHAQDX4A7fYRFPkMLMMFvDCVebjcjoSW2gJw

Merkle Root

654753d5148dd7dcd6c48d1e23772e16dd4b9fde3357c56930caf7561d03b811
Transactions (1)
Coinbase654753d5148dd7…caf7561d03b811
1 in β†’ 1 out10.2800 XPM109 B
AQDX4A7f…joSW2gJw
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.

4.463 Γ— 10⁹⁰(91-digit number)
44630084897127294170…95249336761005215079
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
4.463 Γ— 10⁹⁰(91-digit number)
44630084897127294170…95249336761005215079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.463 Γ— 10⁹⁰(91-digit number)
44630084897127294170…95249336761005215081
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
8.926 Γ— 10⁹⁰(91-digit number)
89260169794254588341…90498673522010430159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.926 Γ— 10⁹⁰(91-digit number)
89260169794254588341…90498673522010430161
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
1.785 Γ— 10⁹¹(92-digit number)
17852033958850917668…80997347044020860319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.785 Γ— 10⁹¹(92-digit number)
17852033958850917668…80997347044020860321
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
3.570 Γ— 10⁹¹(92-digit number)
35704067917701835336…61994694088041720639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.570 Γ— 10⁹¹(92-digit number)
35704067917701835336…61994694088041720641
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
7.140 Γ— 10⁹¹(92-digit number)
71408135835403670672…23989388176083441279
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:57,685,970 XPMΒ·at block #6,805,236 Β· updates every 60s
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