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Block #597,941

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/22/2014, 9:15:37 AM Β· Difficulty 10.9307 Β· 6,204,613 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
476716d5b8c03df7882f88a5a86a92b732db23a1ad303487e27978f40ac9c0ad
View on Chainz β†—

Height

#597,941

Difficulty

10.930714

Transactions

2

Size

547 B

Version

2

Bits

0aee434b

Nonce

50,808,834

Timestamp

6/22/2014, 9:15:37 AM

Confirmations

6,204,613

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

171f8c924813330ce617a084e2c1fd62aa11f88d9b6f67e3d12b6e3a4c20d38b
Transactions (2)
Coinbaseeab51e9820f356…c5a02f36644d20
1 in β†’ 1 out8.3700 XPM116 B
ANSXnLY2…Sd25TjkD
dd45231f0d12a5…1a6082dc4573e0
2 in β†’ 1 out33.9900 XPM339 B
APBbaMm6…HFivyeVS
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.

9.223 Γ— 10⁹⁹(100-digit number)
92230301243931293525…84737835253457484799
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
9.223 Γ— 10⁹⁹(100-digit number)
92230301243931293525…84737835253457484799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.223 Γ— 10⁹⁹(100-digit number)
92230301243931293525…84737835253457484801
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
1.844 Γ— 10¹⁰⁰(101-digit number)
18446060248786258705…69475670506914969599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.844 Γ— 10¹⁰⁰(101-digit number)
18446060248786258705…69475670506914969601
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
3.689 Γ— 10¹⁰⁰(101-digit number)
36892120497572517410…38951341013829939199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.689 Γ— 10¹⁰⁰(101-digit number)
36892120497572517410…38951341013829939201
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
7.378 Γ— 10¹⁰⁰(101-digit number)
73784240995145034820…77902682027659878399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.378 Γ— 10¹⁰⁰(101-digit number)
73784240995145034820…77902682027659878401
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
1.475 Γ— 10¹⁰¹(102-digit number)
14756848199029006964…55805364055319756799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.475 Γ— 10¹⁰¹(102-digit number)
14756848199029006964…55805364055319756801
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:57,664,445 XPMΒ·at block #6,802,553 Β· updates every 60s
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