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Block #2,173,707

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/23/2017, 12:36:14 PM Β· Difficulty 10.9098 Β· 4,671,236 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8e16ef0898fc312e642c02e0939b775f61bad8e6c56e7bd6d34a6cb6c56e0ba5
View on Chainz β†—

Height

#2,173,707

Difficulty

10.909782

Transactions

1

Size

201 B

Version

2

Bits

0ae8e775

Nonce

237,304,847

Timestamp

6/23/2017, 12:36:14 PM

Confirmations

4,671,236

Mined by

⛏️ P2SHAWjLSDAbFutDTLabgCL8RvTguPf2zVDmG9

Merkle Root

682f7edb189a845cbf1c3008a867e3a02f00985ba88009db262c8faa6ea845c9
Transactions (1)
Coinbase682f7edb189a84…2c8faa6ea845c9
1 in β†’ 1 out8.3900 XPM110 B
AWjLSDAb…f2zVDmG9
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.

1.826 Γ— 10⁹⁷(98-digit number)
18263709983543422441…88295007471362478079
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
1.826 Γ— 10⁹⁷(98-digit number)
18263709983543422441…88295007471362478079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.826 Γ— 10⁹⁷(98-digit number)
18263709983543422441…88295007471362478081
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
3.652 Γ— 10⁹⁷(98-digit number)
36527419967086844883…76590014942724956159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.652 Γ— 10⁹⁷(98-digit number)
36527419967086844883…76590014942724956161
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
7.305 Γ— 10⁹⁷(98-digit number)
73054839934173689766…53180029885449912319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.305 Γ— 10⁹⁷(98-digit number)
73054839934173689766…53180029885449912321
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
1.461 Γ— 10⁹⁸(99-digit number)
14610967986834737953…06360059770899824639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.461 Γ— 10⁹⁸(99-digit number)
14610967986834737953…06360059770899824641
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
2.922 Γ— 10⁹⁸(99-digit number)
29221935973669475906…12720119541799649279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.922 Γ— 10⁹⁸(99-digit number)
29221935973669475906…12720119541799649281
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:58,003,959 XPMΒ·at block #6,844,942 Β· updates every 60s
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