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Block #195,902

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/6/2013, 3:24:17 AM Β· Difficulty 9.8803 Β· 6,600,047 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7f95c4eaa77907f497a7013729ecdb8a2a590a8294a6998581e84521fb0a3420
View on Chainz β†—

Height

#195,902

Difficulty

9.880333

Transactions

2

Size

358 B

Version

2

Bits

09e15d87

Nonce

352,264

Timestamp

10/6/2013, 3:24:17 AM

Confirmations

6,600,047

Mined by

⛏️ P2SHAYc3QGYaSv1sA3FuuZuBoiE4ttSWDuszQp

Merkle Root

7b40e90bff00a5e5ae0441e36df0430c82c210884b6ba7ebf77e30b6c480dc1c
Transactions (2)
Coinbaseee331001232957…e75158cac8c442
1 in β†’ 1 out10.2400 XPM109 B
AYc3QGYa…SWDuszQp
3fdf2fc09bc13c…044d9d306565fc
1 in β†’ 1 out10.2300 XPM159 B
ASjVcQsq…FrQb84FV
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.

2.667 Γ— 10⁹⁴(95-digit number)
26676890376950467167…06020713064829655999
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
2.667 Γ— 10⁹⁴(95-digit number)
26676890376950467167…06020713064829655999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.667 Γ— 10⁹⁴(95-digit number)
26676890376950467167…06020713064829656001
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
5.335 Γ— 10⁹⁴(95-digit number)
53353780753900934334…12041426129659311999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.335 Γ— 10⁹⁴(95-digit number)
53353780753900934334…12041426129659312001
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
1.067 Γ— 10⁹⁡(96-digit number)
10670756150780186866…24082852259318623999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.067 Γ— 10⁹⁡(96-digit number)
10670756150780186866…24082852259318624001
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
2.134 Γ— 10⁹⁡(96-digit number)
21341512301560373733…48165704518637247999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.134 Γ— 10⁹⁡(96-digit number)
21341512301560373733…48165704518637248001
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
4.268 Γ— 10⁹⁡(96-digit number)
42683024603120747467…96331409037274495999
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:57,611,681 XPMΒ·at block #6,795,948 Β· updates every 60s
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