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Block #512,073

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/26/2014, 3:46:26 PM Β· Difficulty 10.8319 Β· 6,314,685 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
76bdcaa270e861cdbac69c1ec9043b53fa79b13ceb9fe293e9e0db003ed5ab0c
View on Chainz β†—

Height

#512,073

Difficulty

10.831900

Transactions

2

Size

686 B

Version

2

Bits

0ad4f769

Nonce

168,639

Timestamp

4/26/2014, 3:46:26 PM

Confirmations

6,314,685

Mined by

⛏️ P2SHAT4me1AvZf8VyvR54NxSRAex8obz6JjojW

Merkle Root

883d46457c4c7bd7fcae2c6650c4d5a670472dca8a8ee00f5a5ac4ec9435f4d6
Transactions (2)
Coinbase6fb874103d7c97…4cecc9d4e6d230
1 in β†’ 1 out8.5200 XPM109 B
AT4me1Av…bz6JjojW
f408eaafd0d9d5…902a7881fcf901
3 in β†’ 1 out23.0390 XPM486 B
AdzavPV3…fsAEz9zy
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.

2.831 Γ— 10⁹⁢(97-digit number)
28317345595767700759…22263110925899861689
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
2.831 Γ— 10⁹⁢(97-digit number)
28317345595767700759…22263110925899861689
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.831 Γ— 10⁹⁢(97-digit number)
28317345595767700759…22263110925899861691
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
5.663 Γ— 10⁹⁢(97-digit number)
56634691191535401519…44526221851799723379
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.663 Γ— 10⁹⁢(97-digit number)
56634691191535401519…44526221851799723381
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
1.132 Γ— 10⁹⁷(98-digit number)
11326938238307080303…89052443703599446759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.132 Γ— 10⁹⁷(98-digit number)
11326938238307080303…89052443703599446761
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
2.265 Γ— 10⁹⁷(98-digit number)
22653876476614160607…78104887407198893519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.265 Γ— 10⁹⁷(98-digit number)
22653876476614160607…78104887407198893521
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
4.530 Γ— 10⁹⁷(98-digit number)
45307752953228321215…56209774814397787039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.530 Γ— 10⁹⁷(98-digit number)
45307752953228321215…56209774814397787041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,858,223 XPMΒ·at block #6,826,757 Β· updates every 60s
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