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Block #175,204

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/22/2013, 3:30:52 AM Β· Difficulty 9.8636 Β· 6,631,416 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5a3ad2d05bc05bc7ff65c6dd32d1ad30b3cc47ae7914b5968a5be407b84008e7
View on Chainz β†—

Height

#175,204

Difficulty

9.863585

Transactions

2

Size

358 B

Version

2

Bits

09dd13e7

Nonce

178,791

Timestamp

9/22/2013, 3:30:52 AM

Confirmations

6,631,416

Mined by

⛏️ P2SHAQDun9hvr39W7oKrYS6tDFnGurAx7jGihJ

Merkle Root

723c6fbf653ad90d1af58dd6dc0446a0819ac836da1b926097ea8638f02f57a4
Transactions (2)
Coinbase62f2f5535ab61e…8e1d060703baf1
1 in β†’ 1 out10.2700 XPM109 B
AQDun9hv…Ax7jGihJ
5f71da2215561d…39179b595f646a
1 in β†’ 1 out10.2500 XPM159 B
AW9LNP94…CwUR8YpX
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.

6.880 Γ— 10⁹⁴(95-digit number)
68805128426658537006…44076964082008356799
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
6.880 Γ— 10⁹⁴(95-digit number)
68805128426658537006…44076964082008356799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.880 Γ— 10⁹⁴(95-digit number)
68805128426658537006…44076964082008356801
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
1.376 Γ— 10⁹⁡(96-digit number)
13761025685331707401…88153928164016713599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.376 Γ— 10⁹⁡(96-digit number)
13761025685331707401…88153928164016713601
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
2.752 Γ— 10⁹⁡(96-digit number)
27522051370663414802…76307856328033427199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.752 Γ— 10⁹⁡(96-digit number)
27522051370663414802…76307856328033427201
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
5.504 Γ— 10⁹⁡(96-digit number)
55044102741326829605…52615712656066854399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.504 Γ— 10⁹⁡(96-digit number)
55044102741326829605…52615712656066854401
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
1.100 Γ— 10⁹⁢(97-digit number)
11008820548265365921…05231425312133708799
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:57,697,060 XPMΒ·at block #6,806,619 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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