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Block #901,210

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/19/2015, 9:40:04 AM Β· Difficulty 10.9418 Β· 5,916,513 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
193270225fd9b2bb5dceb2f5b55b93d8e5d20648be797646cf4f1746b08f99c3
View on Chainz β†—

Height

#901,210

Difficulty

10.941770

Transactions

2

Size

2.15 KB

Version

2

Bits

0af117d5

Nonce

319,130,906

Timestamp

1/19/2015, 9:40:04 AM

Confirmations

5,916,513

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c273d1b4988ff1fb9ff08700c851f4efd49d9fad9f57ae3da7b18475174eafef
Transactions (2)
Coinbaseea4446f2feef86…45bf64f2a6396c
1 in β†’ 1 out8.3700 XPM116 B
ANSXnLY2…Sd25TjkD
d45fca0ea1d46f…439d5fa71a037b
13 in β†’ 2 out295005.6848 XPM1.95 KB
AJW6nWgY…c76jJbAnAHkLnmhB…LtZqRzFC
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.

1.770 Γ— 10⁹⁡(96-digit number)
17702781606348351045…46196225389378696599
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
1.770 Γ— 10⁹⁡(96-digit number)
17702781606348351045…46196225389378696599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.770 Γ— 10⁹⁡(96-digit number)
17702781606348351045…46196225389378696601
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
3.540 Γ— 10⁹⁡(96-digit number)
35405563212696702091…92392450778757393199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.540 Γ— 10⁹⁡(96-digit number)
35405563212696702091…92392450778757393201
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
7.081 Γ— 10⁹⁡(96-digit number)
70811126425393404183…84784901557514786399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.081 Γ— 10⁹⁡(96-digit number)
70811126425393404183…84784901557514786401
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
1.416 Γ— 10⁹⁢(97-digit number)
14162225285078680836…69569803115029572799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.416 Γ— 10⁹⁢(97-digit number)
14162225285078680836…69569803115029572801
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
2.832 Γ— 10⁹⁢(97-digit number)
28324450570157361673…39139606230059145599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.832 Γ— 10⁹⁢(97-digit number)
28324450570157361673…39139606230059145601
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:57,785,843 XPMΒ·at block #6,817,722 Β· updates every 60s
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