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Block #1,762,898

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/14/2016, 4:05:34 PM Β· Difficulty 10.7382 Β· 5,047,955 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1c5797ada5ea80d3b5b6c6839793aad5ae265e9ac6643528a2ab5ceefec4b72b
View on Chainz β†—

Height

#1,762,898

Difficulty

10.738218

Transactions

2

Size

425 B

Version

2

Bits

0abcfbdf

Nonce

754,564,732

Timestamp

9/14/2016, 4:05:34 PM

Confirmations

5,047,955

Mined by

⛏️ P2SHAQk6aFyQisS5S5oEWFpJGyLuHe6Hi89tJi

Merkle Root

6c6b6e7532c92850968a997279d535c64b85f3e7352350ac5a9ae465936a274d
Transactions (2)
Coinbase27fe22c1ca9181…e498f7360eccaa
1 in β†’ 1 out8.6700 XPM110 B
AQk6aFyQ…6Hi89tJi
af6e6285e2eea7…0191ab7e554a8a
1 in β†’ 2 out19999.9900 XPM225 B
ALrScL8r…nTbSz3FLAZAcmTyU…wvLRDq1g
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.

1.334 Γ— 10⁹⁡(96-digit number)
13346380292914554124…02260840912827269119
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
1.334 Γ— 10⁹⁡(96-digit number)
13346380292914554124…02260840912827269119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.334 Γ— 10⁹⁡(96-digit number)
13346380292914554124…02260840912827269121
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
2.669 Γ— 10⁹⁡(96-digit number)
26692760585829108249…04521681825654538239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.669 Γ— 10⁹⁡(96-digit number)
26692760585829108249…04521681825654538241
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
5.338 Γ— 10⁹⁡(96-digit number)
53385521171658216498…09043363651309076479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.338 Γ— 10⁹⁡(96-digit number)
53385521171658216498…09043363651309076481
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
1.067 Γ— 10⁹⁢(97-digit number)
10677104234331643299…18086727302618152959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.067 Γ— 10⁹⁢(97-digit number)
10677104234331643299…18086727302618152961
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
2.135 Γ— 10⁹⁢(97-digit number)
21354208468663286599…36173454605236305919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.135 Γ— 10⁹⁢(97-digit number)
21354208468663286599…36173454605236305921
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:57,730,920 XPMΒ·at block #6,810,852 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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