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Block #106,596

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/9/2013, 2:42:39 AM Β· Difficulty 9.6102 Β· 6,702,775 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
873d6631e3ac6fba3432584ac6ae1290f996466991ea0e5542e0e3ba2737451d
View on Chainz β†—

Height

#106,596

Difficulty

9.610167

Transactions

4

Size

1.06 KB

Version

2

Bits

099c33e8

Nonce

62,966

Timestamp

8/9/2013, 2:42:39 AM

Confirmations

6,702,775

Mined by

⛏️ P2SHAYkoKAQ4RDKGS7byjZXQArv3A5uuj8DeZs

Merkle Root

c5ae3cbb0fd4f8ba63a28a10fb82d2002948cb551e06cb468aa86209bde34d99
Transactions (4)
Coinbase67d273265c399f…a924f70a13f24d
1 in β†’ 1 out10.8400 XPM109 B
AYkoKAQ4…uuj8DeZs
dd7ad11a69fcd0…374ff393dfbac9
2 in β†’ 1 out22.1300 XPM273 B
AXkGUvU8…3ZLG8EHC
4d4732baa4be65…833f21fdc90873
1 in β†’ 1 out11.0800 XPM158 B
AXkGUvU8…3ZLG8EHC
8f09610cce5a62…f2ffc146c7eedc
3 in β†’ 1 out11.1400 XPM452 B
AXGg13jX…xq9Bq7T1
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.

8.565 Γ— 10⁹⁷(98-digit number)
85656037254009170750…84136064187965889499
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
8.565 Γ— 10⁹⁷(98-digit number)
85656037254009170750…84136064187965889499
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.565 Γ— 10⁹⁷(98-digit number)
85656037254009170750…84136064187965889501
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
1.713 Γ— 10⁹⁸(99-digit number)
17131207450801834150…68272128375931778999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.713 Γ— 10⁹⁸(99-digit number)
17131207450801834150…68272128375931779001
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
3.426 Γ— 10⁹⁸(99-digit number)
34262414901603668300…36544256751863557999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.426 Γ— 10⁹⁸(99-digit number)
34262414901603668300…36544256751863558001
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
6.852 Γ— 10⁹⁸(99-digit number)
68524829803207336600…73088513503727115999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.852 Γ— 10⁹⁸(99-digit number)
68524829803207336600…73088513503727116001
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
1.370 Γ— 10⁹⁹(100-digit number)
13704965960641467320…46177027007454231999
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:57,719,037 XPMΒ·at block #6,809,370 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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